Final answer:
The interval [0, ∞) is a valid interval representing all real numbers from 0 upwards, not including infinity. It is used in the context of histograms to establish class intervals for graphically representing data frequencies and their distribution.
Step-by-step explanation:
The interval [0, ∞) denotes the set of all real numbers from 0 to infinity, including 0 but not infinity because it is an open interval on the right side. This is indeed an interval, and in the context of histograms, class intervals are used to represent data graphically. However, the rules for including data values in class intervals can vary: some histograms may count a value in a class interval if it falls on the left boundary but not if it falls on the right boundary, except possibly in special cases like the first interval.
Data values that fall on the boundaries determine how the data should be grouped into intervals on a histogram, affecting the skewed distribution representation. For a data set, with the smallest value of 1 and the largest value of 6, choosing boundaries such as 0.5 (for the lower end) and 6.5 (for the upper end) can ensure all values are included in the histogram when setting up the class intervals and bins.